FCNC-induced semileptonic decays of $J/\psi$ in the Standard Model

TL;DR

This paper calculates form factors for FCNC-induced semileptonic $J/ar{D}$ decays using QCD sum rules, predicts very small branching ratios within the Standard Model, and discusses potential implications for new physics detection.

Contribution

It provides a detailed formulation of the $<J/|T_{}| ar{D}^{*0}>$ matrix element and applies QCD sum rules to estimate decay rates, extending previous analyses.

Findings

Branching ratios are too small for current detection.

Form factors are calculated using QCD sum rules.

Potential to identify new physics if deviations are observed.

Abstract

In this work, we calculate the form factors for $J/\psi\to \bar{D}^{(*)0}$ induced by the flavor changing neutral currents (FCNC) in terms of the QCD sum rules. Making use of these form factors, we further calculate the branching fractions of semileptonic decays $J/\psi \to \bar{D}^{(*)0} l ^+ l^-$ ($l=e, \mu$). In particular, we formulate the matrix element $<J/\psi|T_{\mu\nu}| \bar{D}^{*0}>$ with $T_{\mu\nu}$ being a tensor current, which was not fully discussed in previous literature. Our analysis indicates that if only the standard model (SM) applies, the production of single charmed mesons at the present electron-positron colliders is too small to be observed even the resonance effects are included, therefore if an anomalous production rates are observed, it would be a hint of new physics beyond SM. Even though the predicted branching ratios are beyond the reach of present facilities which can be seen from a rough order estimate, the more accurate formulation of the three point correlation function derived in this work has theoretical significance and the technique can also be applied to other places. In analog to some complicated theoretical derivations which do not have immediate phenomenological application yet, if the future experiments can provide sufficient luminosity and accuracy, the results would be helpful.